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"compare to" or "compare with"

When I speak or write, I sometimes am not sure which phrasal verb to use, "compare to" or "compare with". Are they interchangable most of the time? What is the difference? Is there a rule to remember it?

For instance, 1. Compared to running, walking is good for people who have knee problems.

2. Andy compared his math teacher with his English teacher and pointed out what they had in common and what they did not.

3. In order to decide which city to tour, we had to compare with each other.

1 and 2 both compare things, why one uses compare to, two uses compare with?
for 3, can I use compare to here? Is it grammatically incorrect or the meaning has changed?

Re: "compare to" or "compare with"

compared with or compared to

Do the following mean the same?
a net loss of 8 compared with the 1990 result. . .
a net loss of 8 compared to the 1990 result. . .

What difference there may seem to be is probably affected by one’s regional background (American or British) – despite the fact that the major English
dictionaries give separate definitions to the two structures. Webster’s Third (1986) and the Oxford Dictionary (1989) both suggest that compared with is
used when the comparison is part of a broad analysis, and compared to when it’s a matter of specifically likening one thing to another. But the distinction is
probably more honored in the breach than the observance. Webster’s English Usage (1989) found little correlation between the two particles and the two
meanings, and that the two meanings were not necessarily separable anyway. It concluded that any tendency to choose compared to for the meaning “liken” could only be demonstrated for the active verb, not when it was passive or just a past participle. The very similar frequencies of compared to and compared with in data from CCAE also suggest that the two constructions are used indifferently in American English. In British English compared with is a good deal more frequent than compared to: the ratio is about 2:1 in BNC data. Also noteworthy is the fact that compared to appears more often than compared with among spoken data and scripted dialogue. This suggests that it’s the more informal of the two constructions, the one you use when speaking off the cuff, rather than when crafting your prose.
The preference for compared with was once underpinned by the latinist’s insistence that with was the only possible particle, because the prefix in
compare is the Latin cum “with.” Like other Latin-derived principles of usage, its influence has been more pervasive in Britain, and helped to underscore the use of compared with. Yet even there, compared is increasingly construed with to, on the analogy of similar words and structures such as likened to and similar to. The regional preferences for construing compared apply also to the adjective comparable. In British usage comparable to and comparable with are both freely used, appearing in the ratio 4:3 in BNC data. American usage meanwhile is strongly inclined to comparable to, by the evidence of CCAE

Re: "compare to" or "compare with"

Hi watermark

This reference from the Free Dictionary is in line with the way I. as a Brit, would have used "compare to" vs "compare with":

compare - definition of compare by the Free Online Dictionary, Thesaurus and Encyclopedia.Usage Note: Compare usually takes the preposition to when it refers to the activity of describing the resemblances between unlike things: He compared her to a summer day. Scientists sometimes compare the human brain to a computer.
It takes with when it refers to the act of examining two like things in order to discern their similarities or differences: The police compared the forged signature with the original. The committee will have to compare the Senate's version of the bill with the version that was passed by the House.

When compare is used to mean "to liken (one) with another," with is traditionally held to be the correct preposition: That little bauble is not to be compared with (not to) this enormous jewel. But to is frequently used in this context and is not incorrect.

Re: "compare to" or "compare with"

Originally Posted by watermark

When I speak or write, I sometimes am not sure which phrasal verb to use, "compare to" or "compare with". Are they interchangable most of the time? What is the difference? Is there a rule to remember it?

For instance, 1. Compared to running, walking is good for people who have knee problems.

2. Andy compared his math teacher with his English teacher and pointed out what they had in common and what they did not.

3. In order to decide which city to tour, we had to compare with each other.

1 and 2 both compare things, why one uses compare to, two uses compare with?
for 3, can I use compare to here? Is it grammatically incorrect or the meaning has changed?

Thank

You could choose one form and use it always, without making many mistakes (if any). I generally prefer "compare to".
By the way, they aren't phrasal verbs; 'compare' is an ordinary verb, and you are trying to decide which preposition to use with it.